Light-force sensor and method for measuring axial optical-trap forces from changes in light momentum along an optic axis

ABSTRACT

An optical trap and method for measuring both transverse and longitudinal forces on a trapped particle. Laser light sources generate first and second light beams that are focused to the trap region in a counter-propagating manner for trapping the particle. Detectors measure changes in power deflections of the light beams leaving the trap region, and changes in power concentrations of the light beams leaving the trap region. A processor calculates the transverse forces on the particle based upon the measured changes in the power deflections of the light beams, and calculates the longitudinal forces on the particle based upon the measured changes in the power concentrations of the light beams. A single beam optical trap and method are also disclosed, where the second optical beam is generated by a reflection of the first optical beam off of the trapped particle.

This application claims the benefit of U.S. Provisional Application No.60/504,067, filed Sep. 19, 2003.

GOVERNMENT GRANT

This invention was made with Government support under grant (Contract)No. GM-32543 awarded by the NIH and grant nos.: MBC-9118482 andDBI-9732140 awarded by the NSF. The Government has certain rights tothis invention.

FIELD OF THE INVENTION

The present invention relates to optical particle trapping, and moreparticularly to a device and method for trapping and manipulating tinyobjects using laser light, and measuring minute forces imparted on theseobjects both in transverse and longitudinal directions.

BACKGROUND OF THE INVENTION

Devices for optically trapping small particles are better known as“optical traps” or “optical tweezers”. The technique relies on theforces created by one or more laser beams that are refracted by amicroscopic object in order to trap, levitate and move that object. Byfocusing a laser beam though a microscope objective lens down to a verysmall spot (focal region), particles with high indices of refraction,such as glass, plastic, or oil droplets, are attracted to the intenseregions of the beam and can be permanently trapped at the beam's focalregion. Biologists are considerably interested in optical traps becauseminute forces can be measured with sub-picoNewton accuracy on thetrapped object. Since such small forces are not accessible byconventional techniques such as scanning-force-microscopy, optical trapshave become a major investigation tool in biology.

One (preferred) method to measure such forces includes capturing andanalyzing the light after interacting with the particle and computingthe change in momentum flux of the light due to interaction with theparticle. Capturing all the light exiting the optical trap can bedifficult, given that a single-beam trap needs highly marginal rays inorder to trap efficiently, but even a high numerical-aperture (NA) lensmay not accept all these rays when they have interacted with theparticle and are deflected farther off the optic axis. In such a case,it can be difficult to capture and analyze all the light leaving theoptical trap. Therefore, to address this issue, dual beam optical trapshave been developed. Conventional counter-propagating beam optical trapshave been used to trap particles, and measure extremely small transverseforces imparted on those particles. See for example, “Optical tweezerssystem measuring the change in light momentum flux”, Rev. Sci. Instrum.,Vol. 73, No. 6, June 2002. Dual-beam traps are also better thansingle-beam traps for trapping particles with higher refractive indices.

One drawback to conventional momentum-sensing optical traps, and inparticular dual beam counter-propagating optical traps, is that theyonly detect and measure transverse forces on the particle (x and ydirections). Conventional optical traps do not detect and measure axialforces on the particle (z direction). Additionally, counter-propagatingoptical traps can be difficult to align, that is, to bring the two beamfoci together at a common point.

There is a need for an optical trap system (and method) that measuresall three components of external forces, and that is easy align.

SUMMARY OF THE INVENTION

It is desirable to obtain all 3 vector components of any external forcethat may be acting on a trapped particle in an optical trap (OT). As animprovement to a counter-propagating beam OT fitted with a transverselight-force sensor, the present invention includes an “axial light-forcesensor” that permits simultaneous (with transverse components)measurement of the axial force component acting on a trapped particle.The invention collects and analyzes the trapping laser light after itpasses through the particle and leaves the vicinity of the trap. Theaxial force is computed from changes in the axial light-momentum fluxwhich, in turn, is computed from observed changes in the spatialdistribution of exit light intensity at the back focal plane of theobjective collection lenses. To this end, the back focal planes arere-imaged onto special light attenuators with “circular” transmissionprofiles. The light, which passes through the patterned attenuators,falls on planar photo-diodes where it produces current signalsproportional to the axial light-momentum fluxes. Any change in themomentum-fluxes due to the particle is equal to the light force on theparticle, and hence equal to the external axial force to be measured.The device is calibrated from measured constant values: the speed oflight, the objective focal length and the power sensitivity of theplanar photo-diode. Calibration is not affected by the shape of theparticle, the power of the lasers, the sharpness of the trap focus, norby the refractive index of the particle.

The present invention is an optical trap device for trapping a particlethat includes at least one laser light source for generating first andsecond light beams, first and second lenses for focusing the first andsecond light beams to a trap region in a counter-propagating manner fortrapping the particle in the trap region, a first detector for measuringchanges in a power deflection and in a power concentration of the firstlight beam leaving the trap region, and a second detector for measuringchanges in a power deflection and in a power concentration of the secondlight beam leaving the trap region.

In another aspect of the present invention, a method of trapping aparticle includes generating first and second light beams, focusing thefirst and second light beams to a trap region in a counter-propagatingmanner for trapping the particle in the trap region, measuring changesin power deflections of the first and second light beams leaving thetrap region, and measuring changes in power concentrations of the firstand second light beams leaving the trap region.

In yet another aspect of the present invention, an optical trap devicefor trapping a particle includes a laser light source for generating afirst light beam, a first lens for focusing the first light beam to atrap region for trapping the particle in the trap region, a second lensfor focusing the first light beam transmitted through the trap regionwherein the particle reflects a portion of the first light beam tocreate a second light beam that is focused by the first lens, a firstdetector for measuring changes in a power deflection and in a powerconcentration of the first light beam leaving the trap region, and asecond detector for measuring changes in a power deflection and in apower concentration of the second light beam leaving the trap region.

In yet one more aspect of the present invention, a method of trapping aparticle includes generating a first light beam, focusing the firstlight beam to a trap region for trapping the particle in the trap regionwherein the particle reflects a portion of the first light beam tocreate a second light beam, measuring changes in power deflections ofthe first and second light beams leaving the trap region, and measuringchanges in power concentrations of the first and second light beamsleaving the trap region.

Other objects and features of the present invention will become apparentby a review of the specification, claims and appended figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a particle trapped in an optical trap.

FIG. 2 is a schematic diagram illustrating the power deflection detectorand circuitry for analyzing the light exiting the optical trap.

FIG. 3 is a diagram illustrating the counter-propagating beam opticaltrap of the present invention.

FIG. 4 is a diagram illustrating the power concentration detector of thepresent invention.

FIG. 5 is a diagram illustrating a first technique for aligning theoptical trap of the present invention.

FIG. 6A is a diagram illustrating a second technique for aligning theoptical trap of the present invention, by deflecting the optical fiberthat delivers the laser beam to the optical trap.

FIG. 6B is a diagram illustrating how the detector surface is disposedat a conjugate to the pivot point of the optical fiber.

FIG. 7A is a side view of the deflecting optical fiber beam alignmenttechnique using piezo actuators to align the laser beams in the opticaltrap.

FIG. 7B is an end view of the deflecting optical fiber beam alignmenttechnique using piezo actuators to align the laser beams in the opticaltrap.

FIG. 8 is a side view of an alternate embodiment of the deflectingoptical fiber beam alignment technique.

FIG. 9 is a side view of a miniaturized and enclosed version of thecounter-propagating beam optical trap of the present invention.

FIG. 10 is a diagram illustrating use of pixel-array detectors anddigital signal processor in force-measuring optical trap apparatus.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is a method and system for measuring the lightforce on a trapped object by detecting the change in light's momentumwhen it interacts with the object.

A ray of light can be thought of as a directed stream of photons, whichcarries with it a momentum flux dP/dt=nW/c, where W is the power (Watts)carried by the ray, c is the speed of light and n is the refractiveindex of the surrounding buffer. In an optical trap containing a pair ofobjective lenses 2 and a particle 4 held therebetween in a trap regiondefined by the focal regions of the lenses, a particular ray[i] may bedeflected by interaction with the particle 4 through angles θ_(i), φ_(i)relative to the optic axis of the trap, as shown in FIG. 1. The reactionforce felt by the trapped particle due to that ray is given by:F _(i) =dP _(i) /dt=(nW _(i) /c)[i sin θ_(i) cos φ_(i+) jsin θ_(i)sinφ_(i+) k(1=cos φ_(i))].  (1)

To compute forces on a trapped particle with many rays passing nearby,it is sufficient to analyze the power of all rays entering and leavingthe vicinity of the trap and sum over them according to Eqn. 1, with thesign convention such that an un-deflected ray cancels its fluxcontribution when it exits. Experimentally, such analysis can beperformed by collecting the exiting rays with another lens opposite thetrapping lens. If that collection lens is a coma-free objective lens(similar to the trap lens), and if it is placed so the trap focus isalso the focus of the collection lens, then a particular version of theAbbe sine condition holds for rays that strike the collection lens.According to this rule, a ray coming from the focus and inclined at anangle θ_(i) to the optic axis will emanate from the back principal planeparallel to the optic axis at a radial distance r from that axis givenbyr_(i)=n sin θ_(i)R_(L)  (2)where R_(L) is the focal length of the collection lens. Combining Eqns.(1) and (2) in x-y coordinates (x=rcos φ and y=rsin φ) and summing overall rays gives an expression for the force on the particle in terms ofthe spatial intensity distributions W(x,y)_(enter) and W(x,y)_(exit) oflight entering and exiting the lenses.F _(x)=(1/R _(L) c)([ΣW _(i) x _(i)]_(enter) −[ΣW _(i) x_(i)]_(exit))  (3a)F _(y)=(1/R _(L) c)([ΣW _(i) y _(i)]_(enter) −[ΣW _(i) y_(i)]_(exit))  (3b)F _(z)=(n/c) {[ΣW _(i) sqrt(1−(r _(i) /nR _(L))²)]_(enter) −[ΣW _(i)sqrt(1−(r _(i) /nR _(L))²)]_(exit)}  (3c)

The distance-weighted sums of the light intensity, ΣW_(i)x_(i) andΣW_(i)y_(i), are called the “power deflections”. These moments of thespatial intensity distribution can be measured by projecting the lightexiting from the collection lens onto a position-sensitivephoto-detector (PSD), also known as a power deflection detector. Suchdetectors are different from quadrant detectors since they comprise onecontinuous diode (i.e. a power deflection sensor/detector) 6, not four.They can be thought of as a planar PIN junction photodiode sandwichedbetween two plate resistors, as shown in FIG. 2. When a light raystrikes a particular point on the detector 6, it liberates holes andelectrons in the reverse-biased diode layer that electrically connectsthe two planar resistors at that point. For each axis (x,y), theresulting current (which is proportional to ray power W_(i)) is dividedbetween the two electrodes 8 at opposite edges of a resistor layerdepending on the distances to each electrode from where the ray strikes.The currents from all rays striking the PSD are thus weighted bydistance from the edges and summed in a linear fashion. An op-ampcircuit 10 such as the one illustrated in FIG. 2 takes the 4 currentsignals (two into the top PSD layer and two out of the bottom) andconverts them into separate signals for x- and y-distance-averagedintensities. Thus, power deflection is a measure of the powers andoff-axis distances of all the light rays forming the light beam. Powerdeflection of the light beam increases if the overall light beam poweruniformly increases and/or if the overall light beam shifts position inthe positive direction, and vice versa.

The signals from a PSD amplifier (FIG. 2) are given byX=ΨΣW _(i) x _(i) /R _(D)  (4a)Y=ΨΣW _(i) y _(i) /R _(D)  (4b)where Ψ is the power responsivity of the PSD photo-diode, R_(D) is thehalf-width of the square PSD detector area, x_(i) and y_(i) are the xand y components of the ray positions, and W_(i) is the power of each ofthose rays.The x and y components of transverse force are given by combining Eqns.3 and 4:F _(x) =ΔX R _(D) /c ΨR _(L)  (5a)F _(y) =ΔY R _(D) /c ΨR _(L)  (5b)where ΔX and ΔY represent changes in the signals from the powerdeflection detector induced by the X and Y components of the forceapplied to the particle.

The signals from a PSD detector can be used directly as the x and yforce components on a trapped particle, provided the input lightmomentum is first nulled. That is, the PSD is pre-positioned, with noobject in the trap, such that the X and Y outputs are zero. For asymmetrical input beam, this act puts the detector on the optic axis.For an asymmetric input beam, nulling the detector shifts the zero-anglereference such that the incoming light flux has zero transverse (x,y)momentum in that frame. When a particle is trapped, only the outputdistribution changes, not the input. Even then, the output distributionremains symmetrical (null outputs) until external forces F_(x) and F_(y)are applied to the trapped particle.

A problem for the light-force sensor derives from the necessity tocollect all the exiting light to calculate the force. A single-beamoptical trap can apply strong radial (x,y) trapping forces, but ratherweak axial (z) forces. Unless the beam is highly convergent and includesthe full set of marginal rays from a high NA objective lens, theparticle may escape out the back (exit) side of a trap due to areflection or light scattering forces on the particle. Thus, to recoverall the exiting light, such a high NA trap requires a high NA collectionlens. However, if an external force acts on the particle, then theoutput rays from the trap will be deflected even farther off axis thanthe input rays. For larger particle displacements, even the highest NAobjectives available may not collect those exiting marginal rays.Therefore, it is preferable (but not necessary) to utilize thelight-momentum method of the present invention using a dual beam opticaltrap, instead of a single beam optical trap, as detailed below.

It is possible, however, to trap particles with lower NA optics by usingcounter-propagating laser beams that converge through opposing lenses toa common focus (i.e. common focal region). Thus the reflected orscattering light force is balanced and the axial escape route isblocked. Such an instrument, a dual counter-propagating beam opticaltrap, has been reduced to practice and is shown schematically in FIG. 3.Vertically polarized light beams from separate diode lasers 12 (e.g. 835nm light, at 200 mW, from SDL 5431 lasers) are sent through polarizingbeam splitters 18, quarter wave plates 16, and objective lenses 2 (e.g.Nikon 60X plan-Apo-water NA 1.2), so that the light beams are circularlypolarized as they encounter particle 4. The exiting light beams arecollected by opposite objective lenses 2, become horizontally polarizedat the opposite quarter wave plates 16, are deflected down by polarizingbeam splitters 18, and are split into a pair of beams (preferablyequally) by non-polarizing beam splitters 20. The first of the pair ofbeams are directed to power deflection detectors 22 (which measuretransverse momentum of the beams) and the second of the pair of beamsare directed to power concentration detectors 24 (which measurelongitudinal momentum of the beams). The particle is preferablycontained in a fluid chamber 14 formed by two coverslips separated byheat-sealed parafilm strips.

The high NA objective lenses 2 have the ability to focus/collecthigh-angle rays, but the laser beams which enter them are kept small indiameter, thus under-filling the back apertures. Therefore the trappingrays form a narrow cone (low NA beam) and the most marginal of theserays can be collected by the opposite lens 2, even when those rays aredeflected outside the initial set of low inclination angles by theapplication of an external force to the particle 4. In this instrument,the transverse forces from the two beams add together, and hence thesignals from power deflection detectors 22 must be summed to give the xand y components of transverse force on the trapped particle:F _(x)=(ΔX ₁ +ΔX ₂)R _(D) /c ΨR _(L)  (6a)F _(y)=(ΔY ₁ +ΔY ₂)R _(D) /c ΨR _(L)  (6b)where ΔX₁ and ΔX₂ represent changes in the signals from the first andsecond detectors respectively induced by the X component of the forceapplied to the particle, and ΔY₁ and ΔY₂ represent changes in thesignals from the first and second detectors respectively induced by theY component of the force applied to the particle.

To obtain the longitudinal force along the optic axis, F_(z), adifferent type of detector is utilized, namely one that measures thepower concentration of the incident beam. The power concentration is ameasure of cross-sectional distribution of the power within the beam. Asthe power of the light beam is concentrated more toward the center ofthe beam, its power concentration is greater. Conversely, as the beampower distribution is more spread out away from the center of the beam,its power concentration is less. Thus, for example, a powerconcentration detector produces a signal that increases or decreases asthe power distribution within the beam becomes more concentrated towardthe center of the beam, and vice versa. One example of a powerconcentration detector is one in which the distance-weight (sensitivity)falls off from the optic axis according to Eq. 3c, for example as sqrt(1−(r/nR_(L))²). Such response is obtained by a power concentrationdetector 24 having an attenuator 28 with a circular transmissionprofile, placed over a planar photodiode 30, as illustrated in FIG. 4.The circular transmission profile T is sqrt (1−(r/nR_(L))²), where r isnow the radial distance from the center of the attenuator. One suchprofile generated numerically as pixels is illustrated in FIG. 4.

If the attenuator 28 is constructed so its pattern radius is nR_(L),then the detector response to light ray_(i) of intensity WI that falls adistance r_(i) from the pattern center will beZ=Ψ′ΣW _(i) sqrt(1−(r _(i) /nR _(L))²)  (7)where Ψ′ is the responsivity of the planar photo-diode. By combiningequations (3c) and (7), the force signal F_(z) is proportional (by aknown factor) to the difference between the signals from the twoopposing axial power concentration photo-detector signals, namely,F _(z)=(n/c)(ΔZ ₁ −ΔZ ₂)/Ψ′.  (8)where ΔZ₁ and ΔZ₂ represent the changes in the signals from the twopower concentration detectors resulting from longitudinal force on thetrapped particle.

In practice, to compensate for differences in laser powers andsensitivities of the axial detector, the difference signal (ΔZ₁−ΔZ₂) ispreferably nulled, by addition of an arbitrary offset, before anyparticle enters the trap. The signals from detectors 22/24 arepreferably sent to a processor 14, which calculates particle forces anddisplacements utilizing the above described equations. Processor 14could be a stand alone device, or a personal computer runningappropriate software.

An advantage of the above described transverse light-force sensor isthat calibration depends only on constant factors such as R_(L) and cthat do not change with experimental conditions. Force is obtained fromthe conservation of linear momentum of light as measured in the farfield. Thus the measurement of force becomes independent of trap/beaddetails such as shape and size of the particle and refractive indices.Unfortunately, for the above described axial force sensor, itscalibration changes with the refractive index of the fluid buffersurrounding the particle. For instance, adding 1 molar NaCl to waterinside the fluid chamber changes its index from 1.334 to 1.343. Such a−1% correction could simply be applied to the values in Eq. 8, exceptthat the circular-profile attenuator is constructed with a particularradius suitable for water (Eq. 7). For typical rays, where r/nR_(L)<0.5,the residual z-force error will be very small, i.e. less than ¼ percent.

Due to changes in room temperature or humidity and its effect on manyoptical parts, an optical trap with dual counter-propagating beamsrequires constant alignment in order to keep the foci (focal regions) ofthe counter-propagating beams coincident. Such alignment involves movingone trap focus to lie on top of the other. To move a focus, either thebeam angle must be steered as it enters the back of the objective lens,or else the whole objective lens must be moved. FIG. 5 illustrates asolution of the latter type, where the optical trap of FIG. 4 ismodified so that one of the objective lenses 2 is movable with apiezo-actuated x-y-z stage 32 to overlap the foci. Other modificationsinclude the addition of second polarizing beam splitters 34 and relaylenses 36. If a particle has been trapped, this means the foci of thetwo counter-propagating beams are close enough to maintain the trap, andthere is insufficient external forces on the particle to break theparticle free. But if the foci are slightly misaligned, then the trapbeams will exert force on each other (trade momentum) via their commoninteraction with the particle.

While an external transverse force on the trapped particle deflects bothexiting beams in the same direction, a transverse misalignment of thefoci causes the exit beams to be deflected in opposite directions. Inthis case, information to correct the alignment error (by moving theobjective lens) may be derived from the differential force signals.Whereas the F_(x) is proportional to the sum of PSD signals ΔX₁+ΔX₂, thex-axis alignment error is proportional to their difference, namelyΔX₁−ΔX₂. To control transverse alignment, an instrument computer uses aproportional-integrative-differential (PID) feedback algorithm to movethe piezo stage based on readings from the transverse force sensors ofpower deflection detectors 22. Here the x-axis error signal is ΔX₁−ΔX₂and the y-axis error signal is ΔY₁−ΔY₂.

Foci may also be misaligned along the optic axis, that is, they may formshort of each other or past each other along the z-axis. In the formercase (falling short), the two beams pull each other forward via theircommon interaction with the trapped particle, and increase both theirforward momenta. Thus both beams get smaller (more concentrated) aboutthe optic axis, increasing their transmission through the patternedattenuators (axial-force sensors). In the latter case (foci formed pasteach other), the beams retard each other and their exit angles widen,decreasing their transmission through the patterned attenuators. Anaxial-alignment error signal can be derived from comparison of currentaxial sensor outputs with a particle in the trap, (Z₁+Z₂)_(full), tothat of a previous measurement when the trap was empty, (Z₁+Z₂)_(empty).However the “empty” measurement is not current and would need to changeif the laser power changes with time. Therefore it is best to normalizethe ΔZ signals by their respective laser powers, as measured by thepower deflection detector “sum” outputs (see FIG. 2). Then, the improvedz-axis error signal becomes:z-error=(Z ₁/Sum₁ +Z ₂/Sum₂)_(full)−(Z ₁/Sum₁ +Z ₂/Sum₂)_(empty).  (9)This axial error signal is processed by the computer's PID algorithm andfed back to the z-axis piezo of the objective XYZ stage 32. Alternately,if an optical fiber is used to deliver the laser beam to the lens 2, thedistance between the delivery end of the optical fiber and the lens 2can be adjusted based on the error signal to align the foci of the twobeams. Such a system corrects temperature drift in the axial alignmentof the foci.

The counter-propagating-beam laser optical trap of the present inventionutilizes specialized photometric sensors placed in (or referenced to)the back focal planes of objective lenses to measure changes in thespatial distribution of light intensity there, changes caused by someaction on the trapped particle. The beam trap manipulates micron-sizedrefracting particles while simultaneously measuring external forces onthat particle via changes in the momentum of the trapping light. Thebeam trap of the present invention can measure pico-Newton externalforces of the particle in all three orthogonal axes.

For example, as illustrated in FIG. 3, a molecule 40 can be attachedbetween particle 4 and a pipette 42, to examine its mechanicalproperties. As the pipette 42 is moved to exert mechanical stresses onthe molecule, the force exerted in the molecule can be measured by theoptical trap. With the present invention, all three force components(F_(x), F_(y), F_(z)) on the trapped particle, and thus on the moleculeattached thereto, can be measured. Calibrations for both transverse andaxial measurements are immune to changes in focus sharpness, particlesize/shape/index, or laser power, and both can be used for alignment ofdual trap beam foci, either against transverse errors or longitudinalerrors. Calibration of the transverse force sensor is immune to changesin refractive index of buffer liquid, whereas longitudinal sensorcalibration is affected slightly.

FIGS. 6A, 6B, 7A, 7B and 8 illustrate an alternate embodiment for thealignment of the optical trap. Instead of moving one of the beams bymoving one of the objective lenses 2, the beam is transversely moved inthe trap (or in any other application) by moving the light beam beforeit reaches the objective lens 2 using an actuator assembly 44 that bendsan optical fiber about a pivot point. Specifically, as shown in FIG. 6A,the optical output of the laser diode 12 is coupled into a low-massoptical fiber 46, which has a generally rigid portion that is moved(driven) with actuators (e.g. piezo-electric devices) to achieve a highfrequency response (>2 kHz). The delivery end 62 of the optical fiber 46is positioned one focal-length (F) away from a positive lens 48 so as toproduce collimated light which enters the back of an infinity-correctedmicroscope objective lens 2. The optical fiber 46 is held at a pivotpoint X (farther from the lens) by a plate, block or other rigid member52, such that the optical fiber pivots about that point (with a bendlength BL) when the actuators move.

Pivot-point X is a conjugate focal point (through the collimating lens48) to a point at the center of the objective lens' back focal plane(BFP), which is a plane perpendicular to the optic axis at back focus ofthe lens. Pivoting the optical fiber in this manner actually tilts theoptical fiber delivery end 62 away from the center of lenses 2 and 48.Yet, this movement causes the angle of light entering the objective lens2 to change (thus steering the trap focus transversely) while the beamremains stationary at the BFP of the objective lens 2 (i.e. the beamrotates about the BFP of lens 2). Thus, the light beam pivots about anoptical pivot point P (at the BFP) as the optical fiber pivots about itsmechanical pivot point X. The advantage of this configuration is that itprovides a faster response time in translating the beam on the far sideof lens 2, as required for constant-position feedback that cancelsBrownian motion in the optical trap.

Calibration stability for the optical trap derives from accuratemeasurement of light-momentum flux irrespective of changes in particlesize, refractive index or trap position. The relay lenses 36 are used tomake the calibration particularly immune to changes in trap position.The expression in Equations 3(a–c) are accurate provided that the raysin FIG. 1 between the right-hand lens 2 and the detector surface arecollimated and on-axis. In practice, however, rays coming out of a lensare seldom perfectly collimated or centered. Indeed for a steered trapshown in FIG. 6A, the rays entering and leaving the lenses aredeliberately made off-axis. The problem of transferring the luminancepattern (intensity distribution) from the lens 2 to the detectors 22/24would be exacerbated by a large distance between the lens and detectorsbecause the pattern wanders further off axis with distance or growslarger/smaller depending on collimation errors. The ideal place to putthe detector to eliminate such effects is at the Back-Focal Plane (BFP)of the lens 2. At that location, changes in trap position relative tothe optic axis will not affect the rendering of angle distributions Eq.1 into spatial distributions on the detectors (Equations 3).Unfortunately the BFP is generally located somewhere inside of a typicalmicroscope objective lens. To effectively place the detectors 22/24inside such a lens, a relay lens 36 is used to project the BFP onto thesurface of the detectors. That is, the detector surfaces of detectors22/24 are disposed at a conjugate focal plane to the BFP of theobjective lens 2 through a separate relay lens 36.

A particular example of a conjugate-plane arrangement that gives nullsensitivity to trap movement is illustrated in FIG. 6B. Here the fiber'spivot-point X is conjugate to the BFP₁ (back focal plane of the first,left-hand, objective lens 2). The light beam from the fiber end does nottranslate at BFP₁, but rather pivots around the optic axis at the BFP₁as the fiber is pivoted. Meanwhile, the optical beam at the optical trap(at the objective lens focus) translates in the object-focal plane inorder to manipulate trapped particles. The two objective lenses 2 areplaced so their object focal planes OFP's are coincident. Therefore, theBFP₂ (back focal plane of the second, right-hand, objective lens 2)becomes conjugate to the BFP₁ and also conjugate to pivot-point X. Thusthe beam of light does not translate at the BFP₂, but instead pivotsaround the optic axis there. In this example, a relay lens 36 of focallength A is placed half way between the BFP₂ and the surface of one ofthe detectors 22/24. A distance of 2A (double the focal length A) isleft on both sides of the relay lens 36 (between BFP₂ and the relay lens36, and between the relay lens 36 and detector 22/24). The BFP₂ istherefore imaged onto the detector surface with unity magnification. Thedetector surface becomes conjugate to BFP₂, and thus to BFP₁, and thusto pivot-point X. The light beam does not translate at the detectorsurface when the optical fiber is pivoted and the optical trap is moved.Once the detector 22/24 is centered on the optic axis of the light beam,the force signal remains null regardless of trap movement if nothing isin the trap to deflect the light beam. In practice, the light beam issplit (as shown in FIG. 5) so that the surfaces of both detector 22 anddetector 24 are conjugate to the pivot-point X.

FIGS. 7A and 7B illustrates an actuator assembly 44 of the presentinvention. The optical fiber 46 is pivoted by placing its delivery endinside a thin metal tube 50 that is clamped or otherwise fixed by plateor block 52. The optical fiber 46 is preferably cemented to the tube 50at its distal end so it moves with the tube-end 54. The optical fiberemits light outward from the tube-end 54 (preferably the tube end andfiber distal end are adjacent or even coincident). The portions of tube50 and optical fiber 46 therein extending from plate/block 52 togetherform a generally rigid portion of the optical fiber, and plate/block 52serves as a support member for pivoting this rigid portion. Electricalsignals are supplied to piezo stack actuators 56 (such as NEC Corp.AE0203D08), which exert forces on and deflect the tube 50 (and opticalfiber 46 therein). Two such actuators 56 preferably act on a hardspherical enlargement 58 (“ball pivot”) of the tube 50, and are arrangedat right angles so as to give orthogonal bending deflections and thussteer the laser-trap beam focus in both transverse dimensions of theobject focal plane. Placing the ball pivot 58 close to the pivot point Xand far from the tube's distal end amplifies the movement of the tubeend 54. Thus a piezo stack that moves a short distance can cause theoptical fiber delivery end to move a large distance. Z-axis adjustmentcan be implemented by moving the entire piezo actuator assembly 44(along with lens 2) via a stage or a third piezo actuator.

FIG. 8 illustrates an alternate embodiment of the actuator assembly 44of the present invention. Depending on the focal length of thecollimating lens 48 and the distance to the BFP, pivot point X may needto be rather close (e.g. <1 cm) to the delivery end 62 of the opticalfiber 46. Therefore, considering the large size of the actuators 56 andspherical enlargement 58, the actuator assembly 44 can be configured asillustrated in FIG. 8, where the optical fiber 46 pivots nearer itsoutput end 62 (i.e. pivot point X is close to the fiber delivery end).With this configuration, actuators 56 push/pull on and bend an outertube 60 (which concentrically surrounds tube 50). The outer tube 60preferably includes a pivot screen 64 disposed at its distal end, whichis an electro-formed metal screen having small square holes. The glassoptical fiber 46 extends out of tube 50 and passes through one of theseholes and rests in the square corner of that hole. Nearby, the opticalfiber 46 is clamped or otherwise secured inside tube 50, which does notmove. Sufficient clearance exists between tubes 50/60 such that theouter tube 60 can bend from the actuator pressure (i.e. pivot aboutpivot point Y), while the inner tube 50 remains straight. Thus, in thisembodiment, it is the inner tube 50 serves as the support member for thegenerally rigid portion of the fiber, and the generally rigid portion ofthe optical fiber is that portion of optical fiber 46 extending out ofinner tube 50. This portion of the optical fiber is generally rigid byeither sufficient reinforcement (separate tube or plastic sheathing) orsmall enough in length relative to its inherent stiffness, such that itgenerally does not bend under the weight of gravity as it pivots. Outertube 60 is affixed to support member 52 and pivots about pivot point Y,which induces the generally rigid portion of optical fiber 46 to pivotabout pivot point X as the optical fiber is deflected by the movement ofthe pivot screen 64. This configuration has two levels ofdistance-amplification over the normal actuator movement: one levelwhere the distal end of the outer tube 60 moves farther than theactuators 56, and another level where the output-end 62 of the opticalfiber 46 moves farther than the pivot screen 64 (at end of the outertube 60).

FIG. 9 illustrates an embodiment of the present invention that allowsfor more precise force/distance measurements that are not hindered byfloor vibration, acoustic noise, and room temperature changes. A largeapparatus on an optical table is especially difficult to isolate fromvibrations if it sits on a floor that people walk on. Air-leg supportson such tables can transmit and even amplify low-frequency floorvibrations (below 5 Hz). Large metal tables also undergo largedimensional changes when the room temperature changes. A steel table1-meter wide can expand over 10,000 nanometers for each 1-degree C risein room temperature. By reducing the optical trap apparatus in size, itbecomes practical to enclose all optical elements in atemperature-controlled metallic shield (to prevent temperature induceddimensional changes, exclude dust particles and block audible roomnoise). Likewise, it becomes possible to hang the apparatus from theceiling by an elastic cord or spring and thus better isolate it frombuilding/floor vibrations, down to a lower frequency cutoff than anoptical table (<1 Hz).

Thus, the above described counter-propagating-beam laser optical trapcan be miniaturized by making five changes: (1) All lens and prismcomponents are reduced to minimum size consistent with laser-beamdiameter. (2) All free-air optical paths are reduced to a minimumlength. (3) The optical breadboard-table is replaced by acustom-machined optical rail. (4) Many parts in the laser conditioningoptics (namely the heating/cooling diode laser mount with collimatinglens and Faraday isolator and anamorphic prism and astigmatismcorrection lens and spatial filter input lens and pinhole filter andspatial filter output lens) are replaced with by single small component,that is, a “butterfly mount” temperature-controlled diode laser coupledto single-mode optical fiber. (5) Finally, the assembled opticalcomponents are enclosed in an aluminum housing with attached heaters(thermostatically controlled to maintain constant housing temperature).Two additional improvements can include: placing the objective lensesand fluid chamber level with or below the optical components so that ifa fluid leak occurs then the salt-buffers will drip downward away fromthe optics, and employing the above described object-focal plane,piezo-electric driven optical beam translators for independenttranslation of the laser-trap foci.

Consistent with the above described miniaturization, optical trap ofFIG. 9 includes a housing 70 (preferably made of aluminum), thetemperature of which is controlled by one or more thermostatic heaters72. The optical components are mounted to an optical rail 74, with theobjective lenses 2, the prism/lens assemblies 76 (which includes thebeam splitters 18, quarter wave plates 16, etc.), the piezo actuatorassemblies 44, the detectors 22/24 and the laser diodes 12 mounted evenwith or above the fluid chamber 26. A CCD camera 78 and visible lightsource 80 can be included for capturing images of the particles throughthe optical chain of objective lenses. An attachment ring 84 and cords86 (e.g. vibration dampening elastic or bungee type chords) are used tosuspend the housing 70.

While longitudinal momentum measurements are more conveniently measuredusing an optical trap with counter-propagating beams as described aboveand shown in FIGS. 3–5 and 9, it should be noted that it is possible toperform such measurements using an optical trap with a single beam, asnow explained below.

An external force on a trapped particle registers as a change in thelight momentum entering vs. leaving the trap. Therefore it is importantto know both the light intensity distribution going into the trap andcoming out, to make a valid force measurement. For transverse forces,this task is simplified by moving the power deflection detectors 22 to aposition that is centered on the undeflected beam. This adjustment ismade with lasers 12 running but no particle in the trap. Morespecifically, the power deflection detectors 22 measure only the lightexiting the trap, not entering it, so they perform only half of theintegration required in Equations 3. This problem is solved by aligningthe detectors on the optic axis so that, when no particle is present inthe trap, the output beams are centered on the detectors and thedifference signals vanish. The light entering the trap carries notransverse momentum in this frame of reference and need not beconsidered even after a particle has been introduced. Only the exitinglight is affected by interaction with the particle.

However there is no way to move a power concentration detector as shownin FIG. 3 so as to null its output when the laser is on and no particleis in the trap. For axial forces, Eq. 3(C) also must be “differenced” inorder to give the proper Z-axis force. The signals for each powerconcentration detector should be performed in 2 steps as follows:measure a signal value Z_(initial) with no particle in the trap, andthen measure a signal value Z_(final) with an object in the trap, andtake the difference ΔZ=Z_(final)−Z_(initial). If this ΔZ=0, then noexternal force is acting on the beam of light detected by thatparticular PSD. Accordingly, Eq. (7) can be modified to read:Z=Ψ′{[ΣW _(i) sqrt(1−(r _(i) /nR _(L))²)]_(final) −[ΣW _(i) sqrt(1−(r_(i) /nR _(L))²)]_(initial})  (10)and the corrected form of Eq. 8 for a single-beam trap might seem to besimplyF _(z)=(n/c)(ΔZ)/Ψ′.  (11)Unfortunately, a further consideration complicates force measurements ina single-beam trap (or for a dual-beam where the laser powers aredifferent). Most trapped particles, such as plastic or silica beads, arenot anti-reflection coated. Therefore a small Fresnel reflectiondevelops at their dielectric/water interface. This reflection of thetrapping beam creates a pressure on a trapped particle that moves itforward in the trap (away from the laser source). At some equilibriumposition, the forward force is balanced by a refraction force. Here theforward momentum of the transmitted light is increased by concentratingthe rays near the optic axis, just enough to balance the momentum kickfrom the reflected light. Placing a particle in a single-beam trap willcause it to settle slightly forward in the trap and increase Z_(final)over Z_(initial), even though there is no external force on theparticle.

There are several possible techniques to deal with this false Z-forcecomponent of the detector signal: First, use a dual-beam optical trapwith two counter-propagating beams of equal power, so the particleremains in the center of the trap. Second, make differentialmeasurements where Z_(initial) is determined from a trapped particle butit is known that the external force on that particle is zero. Then,apply the external force and measure Z_(final). Such a technique may beinconvenient to use in practice. Third, use a single beam, but use twopower deflection detectors 22 and two power concentration detectors 24in a similar manner as shown in FIG. 3 (i.e. essentially omit one of thelasers 12 from the configuration of this figure). This third techniqueis now explained in more detail.

The detectors 22/24 of FIG. 3 measure the transmitted light from theopposite-side laser. However, with the arrangement of the quarter-waveplates 16, any reflected light from a particle is collected by thenear-side objective lens 2 and directed back into the near-sidedetectors 22/24. The reflected light is therefore correctly counted asmomentum flux to compute force. Thus, by omitting one of the lasers fromthe configuration of FIG. 3, one set of detectors 22/24 is used tomeasure the transmitted light and the other set of detectors 22/24 isused to measure the reflected light. To measure Z-force in such aconfiguration, the Z_(initial) signal is first obtained for bothtransmitted and reflected light with no particle in the trap. Then, aparticle is trapped that is subject to an arbitrary external force,where the Z_(final) signal is measured for both the transmitted andreflected light according to:Z _(transmitted) =Z _(transmitted-final) −Z_(transmitted-initial)  (12a)Z _(reflected) =Z _(reflected-final) −Z _(reflected-initial)  (12b)Thus, the force signal F_(z) is:F _(z)=(n/c)(ΔZ _(transmitted) −ΔZ _(reflected))/Ψ′.  (13)This is physically the same measurement as that of the dual-beam opticaltrap according to Eq. 8.

It should be noted that each set of detectors 22/24 can be combined intoa single detector that measures both transverse and longitudinalmomentum of the light beam. More specifically, the power deflectiondetector 22, the power concentration detector 24 and the beam splitter20 can be replaced with a single detector 90 as shown in FIG. 10.Detector 90 includes a 2-dimensional array of light-sensitive elements(pixels) with an appropriate electronic read-out interface. The pixelintensities could be read into a computer or control circuit wherecalculation of forces are made numerically by weighting the individualpixel intensities by their distances from the optic axis, and combiningthem according to Eq. 3. Alternately, the pixel intensities could beprocessed locally (on the detector chip) to extract moments of thepixel-intensity distribution. In using detector 90, W_(i) would be thelight intensity at a specific pixel, the distance x_(i) would correspondto the x-coordinate of that pixel (relative to center=0), the distancey_(i) would be its y-coordinate, and its radius would be given byr_(i)=sqrt(x_(i) ²+y_(i) ²). A CCD television camera and frame-grabberwould suffice for collecting such data, especially if the frequencyresponse (including exposure, readout and computation time) exceeds 5000Hz in order to cancel Brownian motion inside the trap. Newly developedhigh-speed cameras and frame grabbers are now available (see for exampleEPIX, Inc, http://www.epixcorp.com/products/pixci_cl3sd.htm). The signalprocessor 100 would then receive digital data from two suchcamera/frame-grabber combinations. A new class of digital PSD (alsocalled “profile sensor”) is available that promises both low cost andhigh speed in a pixel-array detector. These detectors pre-process thepixel data on the same chip as the pixel array so as to reduce theamount of serial data that needs to be sent to the computer, i.e., theframe-grabber-processor function is “built-in” (see for example,Hamamatsu (Solid State Division) Profile Sensor S9132 Preliminary DataSheet January, 2004; and “High Speed Digital CMOS 2D Optical PositionSensitive Detector” by Massari et al. at the European Solid StateCircuit Conference (ESSCIRC) in 2002, available online athttp://www.itc.it/soi_publications/pub/43.pdf).

It is to be understood that the present invention is not limited to theembodiment(s) described above and illustrated herein, but encompassesany and all variations falling within the scope of the appended claims.For example, as used herein, collimating lenses or lenses that collimatesimply make a diverging or converging light beam more collimated, and donot necessarily make the resulting light beam perfectly collimated.Therefore, as used herein, a collimated beam is one that is lessdiverging/converging than it was before passing through a collimatinglens. A single lens could include a plurality of lenses, and vice versa.A single laser device could produce the pair of counter-propagatinglight beams (e.g. by using a beam splitter), instead of two lightsources shown in FIG. 3. While actuators 56 are preferablypiezo-electric devices, they could be any conventional mechanical devicefor moving or applying force onto the optical fiber. The generally rigidportions of optical fiber 46 between the pivot point X and the opticalfiber output end 62 need not necessarily be straight, but should besufficiently rigid to preserve the exit angle of the beam relative tothe optical fiber as the optical fiber pivots. The screen 64 could bereplaced by a ledge, an eyelet, a constricted end, or simply omittedaltogether (should the end of outer tube 60 sufficiently control therigid portion of the optical fiber). For the above described equationsand the single or dual beam device of FIG. 3, one in the art willappreciate that if the focal lengths R_(L) of the collection lenses areunequal, or the power responsitivities Ψ of the power deflectiondetectors 22 are unequal, or the power responsitivities Ψ′ of the powerconcentration detectors 22 are unequal, or the half-width of the squarearea R_(D) of the power deflection detectors 22 are unequal, then theequations discussed above can be expanded accordingly. For example,equation 6a (F_(x)=(ΔX₁+ΔX₂) R_(D)/c ΨR_(L)) is a short hand expressionfor F_(x)=ΔX₁R_(D1)/cΨ₁R_(L2)+ΔX₂R_(D2)/cΨ₂R_(L1), and equation 6b(F_(y)=(ΔY₁+ΔY₂) R_(D)/c ΨR_(L)) is a short hand expression forF_(y)=ΔY₁R_(D1)/cΨ₁R_(L2)+ΔY₂R_(D2)/cΨ₂R_(L1), to accommodate anyunequal characteristics of the first and second lenses 2, first andsecond power deflection detectors 20, and first and second powerconcentration detectors 24. For differing focal length objective lenses,the patterned attenuators 28 may need to be different as well. Theportion of optical fiber 46 between the pivot point X and the opticalfiber output end 62 need not be straight, but should be rigid topreserve the exit angle of the beam from the optical fiber. Lastly, ifthe above described detectors are not nulled by centering them on thebeam, then nulling can be performed by subtracting from the signals thatportion of the signal that exists caused by the non-centered beam (i.e.measure signal using light beam without particle in trap, or fromparticle in trap with no forces thereon).

1. An optical trap device for trapping a particle, the devicecomprising: at least one laser light source for generating first andsecond light beams; first and second lenses for focusing the first andsecond light beams to a trap region in a counter-propagating manner fortrapping the particle in the trap region; a first detector for measuringchanges in a power deflection and in a power concentration of the firstlight beam leaving the trap region; and a second detector for measuringchanges in a power deflection and in a power concentration of the secondlight beam leaving the trap region.
 2. The optical trap device of claim1, wherein: the first detector includes a first power deflectiondetector and a first power concentration detector; and the seconddetector includes a second power deflection detector and a second powerconcentration detector.
 3. The optical trap device of claim 2, whereinthe first and second power concentration detectors each comprise: aphoto-diode detector; and an attenuator with a circular transmissionprofile of increasing or decreasing light transmission T as a functionof distance from a center of the attenuator.
 4. The optical trap deviceof claim 3, wherein the transmission T of the attenuator decreases as afunction of distance r from the center of the attenuator according to:T=sqrt(1−(r/nR _(L))²).
 5. The optical trap device of claim 1, furthercomprising: a processor for calculating a transverse force on theparticle based upon the measured changes in the power deflections of thefirst and second light beams, and for calculating a longitudinal forceon the particle based upon the measured changes in the powerconcentrations of the first and second light beams.
 6. The optical trapdevice of claim 5, wherein: the first and second detectors produce firstand second signals that change in response to the measured powerdeflection changes of the first and second light beams; and theprocessor calculates the transverse force on the particle by multiplyingthe changes in the first and second signals by a ratio 1/cR_(L), whereR_(L) is a focal length of at least one of the first and second lensesand c is the speed of light.
 7. The optical trap device of claim 5,wherein: the first and second detectors produce first and second signalsthat change in response to the measured power deflection changes of thefirst and second light beams; and the processor calculates thetransverse force on the particle by multiplying the changes in the firstand second signals by a ratio R_(D)/cΨR_(L), where Ψ is a powerresponsitivity, and R_(D) is a square area half-width, of at least oneof the first and second detectors, R_(L) is a focal length of at leastone of the first and second lenses, and c is the speed of light.
 8. Theoptical trap device of claim 5, wherein: the first detector producesfirst and second signals that change by ΔX₁ and ΔY₁ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the first light beam; the second detector producesthird and fourth signals that change by ΔX₂ and ΔY₂ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the second light beam; and the processor calculatesthe transverse force on the particle by: calculating a first componentF_(x) of the transverse force according toF _(x) =ΔX ₁ R _(D1) /cΨ ₁ R _(L2) +ΔX ₂ R _(D2) /cΨ ₂ R _(L1), andcalculating a second component F_(y) of the transverse force accordingtoF _(y) =ΔY ₁ R _(D1) /cΨ ₁ R _(L2) +ΔY ₂ R _(D2) /cΨ ₂ R _(L1), wherein:Ψ₁ is a power responsitivity, and R_(D1) is a square area half-width, ofthe first detector, Ψ₂ is a power responsitivity, and R_(D2) is a squarearea half-width, of the second detector, R_(L1) is a focal length of thefirst lens R_(L2) is a focal length of the second lens, and c is thespeed of light.
 9. The optical trap device of claim 5, the first andsecond detectors produce first and second signals that change inresponse to the measured power concentration changes of the first andsecond light beams; and wherein the processor calculates thelongitudinal force on the particle by multiplying the changes in thefirst and second signals by n/cΨ′, where Ψ′ is a power responsitivity ofat least one of the first and second detectors, n is a refractive indexof buffer fluid around the particle, and c is the speed of light. 10.The optical trap device of claim 5, wherein: the first detector producesa first signal that changes by ΔZ₁ in response to the measured powerconcentration change of the first light beam; the second detectorproduces a second signal that changes by ΔZ₂ in response to the measuredpower concentration change of the second light beam; and the processorcalculates the longitudinal force F_(z) on the particle according toF_(z)=(n/c)(ΔZ₁−ΔZ₂)/Ψ′, where n is a refractive index of buffer fluidaround the particle and Ψ′ is a power responsitivity of at least one ofthe first and second detectors.
 11. The optical trap device of claim 5,wherein: the first detector produces a first signal that changes fromZ_(1empty) to Z_(1full) in response to the particle entering the trapregion and the measured power concentration change of the first lightbeam; the second detector produces a second signal that changes fromZ_(2empty) to Z_(2full) in response to the particle entering the trapregion and the measured power concentration change of the second lightbeam; and the processor generates an error signal{(Z₁+Z₂)_(full)−(Z₁+Z₂)_(empty)} for moving a focus of the first lightbeam in the trap region relative to a focus of the second light beam inthe trap region.
 12. The optical trap device of claim 11, furthercomprising: a stage for moving the first lens, or an optical fiber enddelivering the first beam to the first lens, in response to the errorsignal.
 13. The optical trap device of claim 1, further comprising: astage for moving the first lens and aligning a focal region of the firstlens with the trap region.
 14. The optical trap device of claim 1,further comprising: optical fibers for delivering the first and secondlight beams to the first and second lenses; and at least one actuatorfor exerting a force on and causing a pivoting of delivery ends of theoptical fibers.
 15. The optical trap device of claim 14, wherein foreach of the optical fibers: a first tube surrounds the delivery end suchthat the at least one actuator exerts the force on the first tube forpivoting the optical fiber delivery end.
 16. The optical trap device ofclaim 15, wherein for each of the optical fibers: a second tubesurrounds the delivery end and is surrounded by the first tube such thatthe first tube pivots the optical fiber delivery end as the first tubeis moved by the at least one actuator.
 17. The optical trap device ofclaim 1, further comprising: a rail on which the first and second lensesand the first and second detectors are mounted; and a fluid chambermounted to the rail and containing the particle, wherein the fluidchamber extends into the trap region.
 18. The optical trap device ofclaim 17, further comprising: a housing containing the rail, the firstand second lenses, the first and second detectors, and the fluidchamber; and a heating device for maintaining an interior of the housingat a predetermined temperature.
 19. The optical trap device of claim 17,wherein the fluid chamber is mounted even with or below the first andsecond lenses.
 20. The optical trap device of claim 1, wherein the firstand second detectors each include a 2-dimensional array oflight-sensitive elements.
 21. A method of trapping a particle,comprising: generating first and second light beams; focusing the firstand second light beams to a trap region in a counter-propagating mannerfor trapping the particle in the trap region; measuring changes in powerdeflections of the first and second light beams leaving the trap region;and measuring changes in power concentrations of the first and secondlight beams leaving the trap region.
 22. The method of claim 21, furthercomprising: calculating a transverse force on the particle based uponthe measured changes in the power deflections of the first and secondlight beams; and calculating a longitudinal force on the particle basedupon the measured changes in the power concentrations of the first andsecond light beams.
 23. The method of claim 22, wherein: the focusing ofthe first and second light beams is performed using first and secondlenses; the measuring of changes in the power deflections is preformedusing first and second detectors that produce first and second signalswhich change in response to the measured power deflection changes of thefirst and second light beams; and the calculation of the transverseforce on the particle includes multiplying the changes in the first andsecond signals by a ratio 1/cR_(L), where R_(L) is a focal length of atleast one of the first and second lenses, and c is the speed of light.24. The method of claim 22, wherein: the focusing of the first andsecond light beams is performed using first and second lenses; themeasuring of changes in the power deflections is performed using firstand second detectors that produce first and second signals which changein response to the measured power deflection changes of the first andsecond light beams; and the calculation of the transverse force on theparticle includes multiplying the changes in the first and secondsignals by a ratio R_(D)/cΨR_(L), where Ψ is a power responsitivity, andR_(D) is a square area half-width, of at least one of the first andsecond detectors, R_(L) is a focal length of at least one of the firstand second lenses, and c is the speed of light.
 25. The method of claim22, wherein: the focusing of the first and second light beams isperformed using first and second lenses; the measuring of changes in thepower deflections is performed using a first detector that producesfirst and second signals which change by ΔX₁ and ΔY₁ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the first light beam; the measuring of changes inthe power deflections is performed using a second detector that producesthird and fourth signals which change by ΔX₂ and ΔY₂ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the second light beam; and the calculation of thetransverse force on the particle includes: calculating a first componentF_(x) of the transverse force according toF _(x) =ΔX ₁ R _(D1) /cΨ ₁ R _(L2) ΔX ₂ R _(D2) /cΨ ₂ R _(L1), andcalculating a second component F_(y) of the transverse force accordingtoF _(y) =ΔY ₁ R _(D1) /cΨ ₁ R _(L2) +ΔY ₂ R _(D2) /cΨ ₂ R _(L1), wherein:Ψ₁ is a power responsitivity, and R_(D1) is a square area half-width, ofthe first detector, Ψ₂ is a power responsitivity, and R_(D2) is a squarearea half-width, of the second detector, R_(L1) is a focal length of thefirst lens R_(L2) is a focal length of the second lens, and c is thespeed of light.
 26. The method of claim 22, wherein: the measuring ofthe changes in power concentrations is performed using first and seconddetectors that produce first and second signals which change in responseto the measured power concentration changes of the first and secondlight beams; and the calculation of the longitudinal force on theparticle includes multiplying the first and second signals by n/cΨ′,where Ψ′ is a power responsitivity of at least one of the first andsecond detectors, n is a refractive index of buffer fluid around theparticle, and c is the speed of light.
 27. The method of claim 22,wherein: the measuring of the changes in power concentrations isperformed using first and second detectors that produce first and secondsignals which change in response to the measured power concentrationchanges of the first and second light beams; and the calculation of thelongitudinal force on the particle includes multiplying a differencebetween the first and second signals by n/cΨ′, where Ψ′ is a powerresponsitivity of at least one of the first and second detectors, n is arefractive index of buffer fluid around the particle, and c is the speedof light.
 28. The method of claim 22, wherein the measuring of thechanges in power concentrations of the first and second light beams isperformed using first and second detectors, the method furthercomprising: attenuating the first and second light beams before reachingthe first and second photo-detectors in a manner that a transmission ofthe first and second light beams increases or decreases as a function ofa distance from a center of the first or second light beams.
 29. Themethod of claim 28, wherein the transmission of the first and secondlight beams decreases as a function of distance r from the center of thefirst or second light beams according to sqrt(1−(r/nR_(L))²).
 30. Themethod of claim 21, wherein the focusing of the first and second lightbeams is performed using first and second lenses, and wherein the firstand second light beams are delivered to the first and second lenses viafirst and second optical fibers, the method further comprising: exertinga force on and causing a pivoting of delivery ends of the first andsecond optical fibers.
 31. The method of claim 21, wherein: producing afirst signal that changes from Z_(1empty) to Z_(1full) in response tothe particle entering the trap region and the measured powerconcentration change of the first light beam; producing a second signalthat changes from Z_(empty) to Z_(2full) in response to the particleentering the trap region and the measured power concentration change ofthe second light beam; and generating an error signal{(Z₁+Z₂)_(full)−(Z₁+Z₂)_(empty)} for moving a focus of the first lightbeam in the trap region relative to a focus of the second light beam inthe trap region.
 32. The method of claim 31, further comprising: movingthe first lens, or an optical fiber end delivering the first beam to thefirst lens, in response to the error signal.
 33. An optical trap devicefor trapping a particle, the device comprising: a laser light source forgenerating a first light beam; a first lens for focusing the first lightbeam to a trap region for trapping the particle in the trap region; asecond lens for collecting the first light beam transmitted through thetrap region, wherein the particle reflects a portion of the first lightbeam to create a second light beam that is collected by the first lens;a first detector for measuring changes in a power deflection and in apower concentration of the first light beam leaving the trap region; anda second detector for measuring changes in a power deflection and in apower concentration of the second light beam leaving the trap region.34. The optical trap device of claim 33, wherein: the first detectorincludes a first power deflection detector and a first powerconcentration detector; and the second detector includes a second powerdeflection detector and a second power concentration detector.
 35. Theoptical trap device of claim 34, wherein the first and second powerconcentration detectors each comprise: a photo-diode detector; and anattenuator with a circular transmission profile of increasing ordecreasing light transmission T as a function of distance from a centerof the attenuator.
 36. The optical trap device of claim 35, wherein thetransmission T of the attenuator decreases as a function of distance rfrom the center of the attenuator according to:T=sqrt(1−(r/nR _(L))²).
 37. The optical trap device of claim 33, furthercomprising: a processor for calculating a transverse force on theparticle based upon the measured changes in the power deflections of thefirst and second light beams, and for calculating a longitudinal forceon the particle based upon the measured changes in the powerconcentrations of the first and second light beams.
 38. The optical trapdevice of claim 37, wherein: the first and second detectors producefirst and second signals that change in response to the measured powerdeflection changes of the first and second light beams; and theprocessor calculates the transverse force on the particle by multiplyingthe changes in the first and second signals by a ratio 1/cR_(L), whereR_(L) is a focal length of at least one of the first and second lensesand c is the speed of light.
 39. The optical trap device of claim 37,wherein: the first and second detectors produce first and second signalsthat change in response to the measured power deflection changes of thefirst and second light beams; and the processor calculates thetransverse force on the particle by multiplying the changes in the firstand second signals by a ratio R_(D)/cΨR_(L), where Ψ is a powerresponsitivity, and R_(D) is a square area half-width, of at least oneof the first and second detectors, R_(L) is a focal length of at leastone of the first and second lenses, and c is the speed of light.
 40. Theoptical trap device of claim 37, wherein: the first detector producesfirst and second signals that change by ΔX₁ and ΔY₁ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the first light beam; the second detector producesthird and fourth signals that change by ΔX₂ and ΔY₂ respectively inresponse to orthogonal x and y components of the measured powerdeflection change of the second light beam; and the processor calculatesthe transverse force on the particle by: calculating a first componentF_(x) of the transverse force according toF _(x) =ΔX ₁ R _(D1) /cΨ ₁ R _(L2) +ΔX ₂ R _(D2) /cΨ ₂ R _(L1), andcalculating a second component F_(y) of the transverse force accordingtoF _(y) =ΔY ₁ R _(D1) /cΨ ₁ R _(L2) +ΔY ₂ R _(D2) /cΨ ₂ R _(L1), wherein:Ψ₁ is a power responsitivity, and R_(D1) is a square area half-width, ofthe first detector, Ψ₂ is a power responsitivity, and R_(D2) is a squarearea half-width, of the second detector, R_(L1) is a focal length of thefirst lens R_(L2) is a focal length of the second lens, and c is thespeed of light.
 41. The optical trap device of claim 37, wherein: thefirst and second detectors produce first and second signals that changein response to the measured power concentration changes of the first andsecond light beams; and wherein the processor calculates thelongitudinal force on the particle by multiplying the changes in thefirst and second signals by n/cΨ′, where Ψ′ is a power responsitivity ofat least one of the first and second detectors, n is a refractive indexof buffer fluid around the particle, and c is the speed of light. 42.The optical trap device of claim 37, wherein: the first detectorproduces a first signal that changes by ΔZ₁ in response to the measuredpower concentration change of the first light beam; the second detectorproduces a second signal that changes by ΔZ₂ in response to the measuredpower concentration change of the second light beam; and the processorcalculates the longitudinal force F_(z) on the particle according toF_(z)=(n/c)(ΔZ₁−ΔZ₂)/Ψ′, where n is a refractive index of buffer fluidaround the particle and Ψ′ is a power responsitivity of at least one ofthe first and second detectors.
 43. The optical trap device of claim 33,further comprising: a stage for moving the first lens and aligning afocal region of the first lens with the trap region.
 44. The opticaltrap device of claim 33, further comprising: an optical fiber fordelivering the first light beam to the first lens; and at least oneactuator for exerting a force on and causing a pivoting of delivery endof the optical fiber.
 45. The optical trap device of claim 44, furthercomprising: a first tube surrounding the delivery end such that the atleast one actuator exerts the force on the first tube for pivoting theoptical fiber delivery end.
 46. The optical trap device of claim 45,further comprising: a second tube that surrounds the delivery end and issurrounded by the first tube such that the first tube pivots the opticalfiber delivery end as the first tube is moved by the at least oneactuator.
 47. The optical trap device of claim 33, further comprising: arail on which the first and second lenses and the first and seconddetectors are mounted; and a fluid chamber mounted to the rail andcontaining the particle, wherein the fluid chamber extends into the trapregion.
 48. The optical trap device of claim 47, further comprising: ahousing containing the rail, the first and second lenses, the first andsecond detectors, and the fluid chamber; and a heating device formaintaining an interior of the housing at a predetermined temperature.49. The optical trap device of claim 47, wherein the fluid chamber ismounted even with or below the first and second lenses.
 50. The opticaltrap device of claim 33, wherein the first and second detectors eachinclude a 2-dimensional array of light-sensitive elements.
 51. A methodof trapping a particle, comprising: generating a first light beam;focusing the first light beam to a trap region for trapping the particlein the trap region, wherein the particle reflects a portion of the firstlight beam to create a second light beam; measuring changes in powerdeflections of the first and second light beams leaving the trap region;and measuring changes in power concentrations of the first and secondlight beams leaving the trap region.
 52. The method of claim 51, furthercomprising: calculating a transverse force on the particle based uponthe measured changes in the power deflections of the first and secondlight beams; and calculating a longitudinal force on the particle basedupon the measured changes in the power concentrations of the first andsecond light beams.
 53. The method of claim 52, wherein: the focusing ofthe first light beam is performed by a first lens such that the focusedfirst light beam is collected by a second lens and the second light beamis collected by the first lens; the measuring of changes in the powerdeflections is performed using first and second detectors that producefirst and second signals which change in response to the measured powerdeflection changes of the first and second light beams; and thecalculation of the transverse force on the particle includes multiplyingthe changes in the first and second signals by a ratio 1/cR_(L), whereR_(L) is a focal length of at least one of the first and second lenses,and c is the speed of light.
 54. The method of claim 52, wherein: thefocusing of the first light beam is performed by a first lens such thatthe focused first light beam is collected by a second lens and thesecond light beam is collected by the first lens; the measuring ofchanges in the power deflections is performed using first and seconddetectors that produce first and second signals which change in responseto the measured power deflection changes of the first and second lightbeams; and the calculation of the transverse force on the particleincludes multiplying the changes in the first and second signals by aratio R_(D)/cΨR_(L), where Ψ is a power responsitivity, and R_(D) is asquare area half-width, of at least one of the first and seconddetectors, R_(L) is a focal length of at least one of the first andsecond lenses, and c is the speed of light.
 55. The method of claim 52,wherein: the focusing of the first light beam is performed by a firstlens such that the focused first light beam is collected by a secondlens and the second light beam is collected by the first lens; themeasuring of changes in the power deflections is performed using a firstdetector that produces first and second signals which change by ΔX₁ andΔY₁ respectively in response to orthogonal x and y components of themeasured power deflection change of the first light beam; the measuringof changes in the power deflections is performed using a second detectorthat produces third and fourth signals which change by ΔX₂ and ΔY₂respectively in response to orthogonal x and y components of themeasured power deflection change of the second light beam; and thecalculation of the transverse force on the particle includes:calculating a first component F_(x) of the transverse force according toF _(x) =ΔX ₁ R _(D1) /cΨ ₁ R _(L2) +ΔX ₂ R _(D2) /cΨ ₂ R _(L1), andcalculating a second component F_(y) of the transverse force accordingtoF _(y) =ΔY ₁ R _(D1) /cΨ ₁ R _(L2) +ΔY ₂ R _(D2) /cΨ ₂ R _(L1), wherein:Ψ₁ is a power responsitivity, and R_(D1) is a square area half-width, ofthe first detector, Ψ₂ is a power responsitivity, and R_(D2) is a squarearea half-width, of the second detector, R_(L1) is a focal length of thefirst lens R_(L2) is a focal length of the second lens, and c is thespeed of light.
 56. The method of claim 52, wherein: the measuring ofthe changes in power concentrations is performed using first and seconddetectors that produce first and second signals which change in responseto the measured power concentration changes of the first and secondlight beams; and the calculation of the longitudinal force on theparticle includes multiplying the first and second signals by n/cΨ′,where Ψ′ is a power responsitivity of at least one of the first andsecond detectors, n is a refractive index of buffer fluid around theparticle, and c is the speed of light.
 57. The method of claim 52,wherein: the measuring of the changes in power concentrations isperformed using first and second detectors that produce first and secondsignals which change in response to the measured power concentrationchanges of the first and second light beams; and the calculation of thelongitudinal force on the particle includes multiplying a differencebetween the first and second signals by n/cΨ′, where Ψ′ is a powerresponsitivity of at least one of the first and second detectors, n is arefractive index of buffer fluid around the particle, and c is the speedof light.
 58. The method of claim 52, wherein the measuring of thechanges in power concentrations of the first and second light beams isperformed using first and second detectors, the method furthercomprising: attenuating the first and second light beams before reachingthe first and second detectors in a manner that a transmission of thefirst and second light beams increases or decreases as a function of adistance from a center of the first or second light beams.
 59. Themethod of claim 58, wherein the transmission of the first and secondlight beams decreases as a function of distance r from the center of thefirst or second light beams according to sqrt(1−(r/nR_(L))²).
 60. Themethod of claim 51, wherein the focusing of the first light beam isperformed using a lens, and wherein the first light beam is delivered tothe lens via an optical fiber, the method further comprising: exerting aforce on and causing a pivoting of a delivery end of the optical fiber.